[EM] Unranked IRV versus Approval - insincere voting strategy in UIRV

[Tom Ruen]

Here's a simple case of interest between these methods. This case makes
UIRV's top bias obvious.

Let A and B be two strong parties, and C is a "weaker" centrist. A and B
supporters are scared and some compromise to C, while C's core supporters
all bullet vote in the middle.

Approval Ballots: A=30%, B=28%, C=22%, AC=10%, BC=10%

Approval: A=40%, B=38%, C=42%
C wins

UIRV:
Round 1: A=35%, B=33%, C=32%
Eliminate C
Round 2: A=40, B=38, NOTA=22
A wins

Now pretend that 2% of voters supporting B decided that B can't win and
instead of compromising, bullet voted for C.

Approval Ballots: A=30%, B=28%, C=24%, AC=10%, BC=8%

Approval: A=40%, B=35%, C=42%

UIRV:
Round 1: A=35%, B=32%, C=33%
Eliminate B
Round 2: A=35, C=37, NOTA=28
C wins

This shows that supporters of the weakest candidate C may be better off
ignoring their favorite in Unranked-IRV and voting fully for their
compromise in order to not have their least favorite candidate win.

Approval empowers voters to vote always vote for one's favorite. UIRV makes
supporting a favorite and a compromise a risky proposition if elimination
order is uncertain.

One other thing's clear now. Approval makes compromise votes more likely to
help a favorite lose. UIRV is more likely to eliminate one or the other to
compete against a polar opposite candidate. I expect educated Voters would
tend to offer compromises less often in Approval.

Pretend here that A supporters were more brave and only half as many
compromised:

Approval Ballots: A=35%, B=28%, C=24%, AC=5% BC=8%

Approval: A=40%, B=38%, C=37%
A wins for standing tall in Approval

In Approval, if you vote for your favorite and compromise, your compromise
has a good chance to beat your favorite.
In Unranked-IRV, if you vote for your favorite and compromise, both are more
likely to lose!

This is the fundamental risk difference in offering compromises. Both are
safe when order is safe and both are dangerous when candidates are close.
Approval is always safe if you really don't care which wins.

In approval, the top two candidates will tend to be similar (rather than
diverse) while in runoffs the top two candidates will tend to be polar
opposites. Another way to look at it, runoffs generate progressively smaller
subsets of candidates which collectively best represent the most voters, but
if you're only electing one, it may not really matter!

Well, that's my best thoughts about the differences for now!


Tom Ruen